Lecture 1 - It's Full of Stars! (1/12/99)

Open cluster M45, the Pleiades, in the constellation Taurus.
(Courtesy SEDS)

Key Question:

How do we find out about
the distant Universe?

Key Principle:

The Electromagnetic Spectrum

Key Problem:

What does light tell us about where
it came from?

Investigations:

Stars, Galaxies and the Universe

How many orders of magnitude is it from the human scale of
1 meter to the edge of our Solar System? To the outermost observable
scale of the Universe?

How do we get our information about the distant universe when we
cannot send space probes to directly sample the conditions as we can
in our own solar system?

What assumptions are critical to our ability to relate results of
experiments on the Earth to what we see in the Universe?

What are examples of the ubiquitous nature of clustering
on all scales in our Universe?

What are some of the wide range of conditions (density, temperature,
pressure, gravity, energy) that we will find out there?

Electromagnetic Waves

What is an electromagnetic wave?

What is the relation between the speed, wavelength, and
frequency of electromagnetic waves in free space?

What is the frequency of a 1-meter radio wave?

What is the frequency of a 1-cm microwave?

What is a typical wavelength for visible light?

What is the difference between radio waves and visible light?

What is the electromagnetic spectrum?

What is a quantum of light?

What is Planck's constant (h)?

What is the energy of a photon of light with a given wavelength?

What is infrared radiation and why do we associate it with
heat?

Why are ultraviolet rays and X-rays more dangerous
to our bodies than visible light and radio waves?

What is a gamma ray and how are they generally generated?

Parallax

How do your eyes use stereo vision to give depth perception?

How does triginometric parallax work?

For what distance does a 1 AU baseline show a parallax of 1 arc
second?

What is stellar parallax?

Which component of the Earth's velocity is relevant for parallax?

What is a parsec?

How do we use parallax to determine distances?

What is the angle subtended by the Earth's orbit at a distance
of 1 parsec?

Goals of this course:

Understand how we came to our current paradigm for the Universe

Construct our own model for the Universe

Build intuition about astrophysical equations

See how new technology and observational facilities push astronomy forward

Discover our place in the larger picture of the Universe

Learn how physics, engineering, mathematics, chemistry, geology and
biology all interact in astronomy

If you missed the first lecture:

No worries. I mostly talked about the stuff in the course guide, and
some of the topics listed above. Oh, and I showed some cool laserdisk
pictures too. You can find photocopies of my lecture notes on reserve
in the Physics, Math & Astronomy Library, 3rd Floor, North Wing, DRL.

The notes summarized below give extra explanations for some of the
key concepts from this lecture:

Electromagnetic Waves:

The electromagnetic wave, as described by Maxwell's equations, consists
of mutually perpendicular harmonic electric and magnetic fields oscillating
in phase and propagating in the orthogonal direction.

Almost everything we know about the Universe has been brought to us by the
light that we observe with our instruments and eyes. Light, radio waves,
radar, X-rays and ultraviolet rays are all examples of the same phenomenon of
electromagnetic radiation. Light can be thought of as a
electromagnetic wave with crests and troughs as in ocean waves (but
without the ocean!). The things that are rising and falling in an
electromagnetic wave are the electric and magnetic "fields", which rise and
fall in step as a function of space and time. If we were to freeze time, and
move along the direction of a wave, we would measure electric and magnetic
forces that increased then decreased then changed direction and back again,
like a sine wave. The distance between crests of the wave is called the
wavelength and is measured in meters (or centimeters or nanometers,
whatever is convenient). If one were to let time move normally, but measure
the electric and magnetic forces as a wave passes by, then we would see the
crests and troughs moving past us at the speed of light. Thus, we would see
the waves pass us at the frequency of a certain number of cycles per
second, say f, given by:

f = c / l

where l is meant to be the wavelength. We are familiar in
using frequency to describe radio waves. When we say our favorite
radio station has a frequency of 100 Megacycles (or MegaHertz), we
mean that f = 100 x 10^6, that is 10^8, cycles per second.
(Remember, mega means 10^6). Note that since the speed of light
c = 3 x 10^8 m/s, that a frequency of 100 megacycles corresponds
to a wavelength l = c/f = 3 meters.

The electric and magnetic forces in an electromagnetic wave are
at right angles (perpendicular) to each other always.

The electric and magnetic forces from an electromagnetic wave,
such as visible light or radio waves, can be measured.
A radio wave, with a wavelength of 1 meter for example, can
cause electrons in a wire of about that same length to move
back and forth due to the oscillating electric force in the wave.
These moving electrons are measureable as an electric current
in the wire - this is how a radio or TV antenna works to receive
signals!

The electrons in the metal of the antenna (which is basically just
a long wire) are free to move a little in response to the radio wave
electric field. The current alternates like a sine wave.
The reverse is also true! If you oscillate the current like a sine
wave in a long wire, an electromagnetic wave of the same frequency
is generated. This is how radio and TV transmitters work.

Light as Photons:

Light can also be thought of as made up of particles, known as
photons. Light is both a wave and a particle at the same time. The
reconciliation of this dual nature has been one of the greatest breakthroughs
in physics at the turn of the century. Each photon has a specific energy
given proportional to the frequency of the wave that it corresponds to. The
energy of a photon of frequency f is:

There are many different energy photons, with energies ranging from zero to
infinity, each corresponding to waves with wavelengths from infintely long to
infintesimally small (zero). This is what is called the electromagnetic
spectrum Radio waves, with wavelengths around 1 meter, are fundamentally
the same as visible light, with wavelength around 500 nanometers (nm), the
same as X-rays, with wavelengths around 1 nm. Because the photon energy is
proportional to frequency, the high frequency, short wavelength radiation like
UV and X-rays and Gamma Rays can actually do major damage to our bodies if we
are exposed to it. It takes many microwaves (wavelength about 1 cm) to cook
food in a microwave oven, because the photons each have very low energy.
Nuclear explosions release large amounts of deadly Gamma Rays, each of which
can do lots of molecular damage when they pass into organic material.

Different materials absorb specific frequencies of light. This is
due to resonances with atomic and molecular structures as we will
see later on. The air in the Earth's atmosphere absorbs the waves
except special "windows" or wavelength bands where it is transparent.
Both visible light and radio waves fall in these windows, so we can
see out from the Earth into the heavens.

Stellar Parallax:

The small angle formula tells us that the angle (in radians) subtended
by an object of diameter D at distance r is:

= D / r

This can be turned around in that if we observe an object shift direction
by this angle (in radians) when we move a distance D perpendicular to its
direction, then it must be at a distance r.

There are 206265 arcseconds (") in a radian, so the angular size
of an object of diameter D at distance r is

" = 206265 * D / r

If we use the baseline of the Earth's orbit (2 AU for 6 months apart) and
see a shift of theta = 2 * p arcseconds, then

r = 206265 AU / p

It is customary to define p as the parallax. Thus a parallax
p of 1" means that the distance r is 206265 AU. If we define the unit of
distance called the parsec to be 1 pc = 206265 AU, then

r = 1 pc / p

A star 1 parsec away has a parallax of 1 arcsecond.
Talk about convenience! Note that 1 pc is about 3.26 light-years.
The nearest star is around 1 pc away.